(i) In the figure shown, the heavy cylinder (radius R) resting on a smooth surface separates two liquids of densities `2rho` and `3rho`. Find the height 'h' for the equilibrium of cylinder.

(ii) The cross section of a dam wall is an arc of a circle of radius R=20m subtending on angle of `theta=60^(@)` at the centre of the circle. the centre (O) of the circle lies in the water surface. The width of the dam (i.e., dimension perpendicular to the figure) is b=10m. Neglect atmospheric pressure is following calculations.

(a) Calculate the vertical component of force `(F_(x))` applied by water on the curved dam wall.
(b) Calculate the horizontal component of force `(F_(H))` applied by water on the curved dam wall.
(c) Calculate the resultant force applied by the water on the curved dam wall.

Answer

(i) `sqrt((3)/(2))R`
(ii) (a) `F_(v)=1.2xx10^(7)N`
(b) `F_(H)=1.5xx10^(7)N`
(c) `F=1.92xx10^(7)N`